Homoclinic flip bifurcations accompanied by transcritical bifurcation (Q1938743)
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scientific article; zbMATH DE number 6138475
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homoclinic flip bifurcations accompanied by transcritical bifurcation |
scientific article; zbMATH DE number 6138475 |
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Homoclinic flip bifurcations accompanied by transcritical bifurcation (English)
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22 February 2013
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The author investigates the bifurcation of a homoclinic loop with a nonhyperbolic equilibrium by constructing a suitable Poincaré map. Using the fundamental solutions to linear variational equations as an active coordinate system, he constructs a global map which is composed of a regular map in the tubular neighborhood of the homoclinic orbit and a singular map near the equilibrium. The bifurcation equation obtained is analyzed to find homoclinic and periodic orbits (Theorems 4.1 and 4.2) and heteroclinic orbits (Theorem 4.3).
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transcritical bifurcation
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homoclinic orbit
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periodic orbit
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local coordinate system
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Poincaré maps
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